A108564 a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 4, for n>3: a(n+1) = SORT[a(n) + a(n-1) + a(n-2) + a(n-3)], where SORT places digits in ascending order and deletes 0's.

0, 1, 1, 2, 4, 8, 15, 29, 56, 18, 118, 122, 134, 239, 136, 136, 456, 679, 147, 1148, 234, 228, 1577, 1378, 1347, 345, 4467, 3577, 3679, 1268, 11299, 12389, 23568, 24458, 11477, 12789, 22279, 137, 24668, 35789, 23788, 23488, 13377, 24469, 12258, 23579

Offset: 0

Author

Jonathan Vos Post, Jun 10 2005

Keywords

• base
• easy
• nonn

Comments

Sorted tetranacci numbers, a.k.a. sorted Fibonacci 4-step sequence.

As found by T. D. Noe: Max=4556699. Cycle period=41652. Cycle starts with the 23944th term.

Examples

			a(8) = SORT[a(4) + a(5) + a(6) + a(7)] = SORT[108] = 18.
a(10) = SORT[a(6) + a(7) + a(8) + a(9)] = SORT[221] = 122.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Richard I. Hess, Problem 920: sorted Fibonacci sequence, Pi Mu Epsilon Journal, Vol. 10 (Fall 1998) No. 9, pp. 754-755.

Crossrefs

Cf. A000078, A069638, A107281, A108565-A108573.

Programs

Mathematica

nxt[{a_,b_,c_,d_,e_}]:={b,c,d,e,FromDigits[Sort[DeleteCases[ IntegerDigits[ b+c+d+e],?0]]]}; NestList[nxt,{0,1,1,2,4},50][[All,1]] (* _Harvey P. Dale, Jan 17 2022 *)